RC discharge time constant

[renzoms]

Are the two underlined equations at the bottom correct (can I calculate an equivalent resistance for the time constant)? I understand how to find voltage and current for each element at time t supplied with DC voltage. So I’m looking at discharging two ways. Are they both appropriately solved?
Also I've just understood Thevenin equivalent circuit(s) solutions to these circuits so I specifically want to know if the time constant can be calculated by an equivalence resistance. Thanks guys I'm excited about every second I'll be a part of this forum!

[T3sl4co1l]

Yes.  In the first case I(R1) = 0 so it only depends on R2, while for the second, R1 and R2 act in parallel.

Note that if we consider the opposite event, the capacitor starting from zero and charging through R1, the resistors also act in parallel, for a number of equivalent reasons (fundamentally, linearity and reciprocity, or superposition; Thevenin's theorem is a direct consequence).

Directly applicable, say to logic circuits, where the output pins have transistors pulling up and down, as the switches shown.  And each switch has its own resistance.  So the RC time constant varies, and you need to be far enough down both time constants to obtain a reasonably square pulse, thus setting a limit on clock rate.

Tim